Oxygen is a consumable. It costs money and I have to go to the hardware store to get it. The Mix-Stir just uses battery charge on a rechargeable drill. It's also easier to clean the mix-stir (marginally). So I use the Mix-Stir when possible.
I use more O2 on bigger batches because I really want to encourage the best growth environment for the yeast.
There's no problem with using O2 on normal batches. It is just faster and less hassle for me to use the Mix-Stir.
I don't have DO measuring equipment so I don't know the difference between the methods. I just found something that reliably works, so that's what I do.
Basically, I try to optimize my process to the point where I can use easier indirect measurements that I know will give me desired results. I know I need to run my O2 full blast for a minute. I know I need to use the Mix-Stir on a certain setting for a certain time. I don't need to measure DO levels because I know following my process for these times will give me what I want.
Sort of like I don't measure my water-to-grist ratio; I do it until it looks right.